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Asymptotic formulas with sharp remainder estimates for bound states of Schrödinger operators, I

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References

  1. S. Agmon,On kernels, eigenvalues and eigenfunctions of operators related to elliptic problems, Comm. Pure Appl. Math.18 (1965), 627–663.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Agmon,Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Israel J. Math.5 (1968), 165–183.

    Google Scholar 

  3. R. Beals,A general calculus of pseudodifferential operators, Duke Math. J.42 (1975), 1–42.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Sh. Birman,On the spectrum of singular boundary problems, Mat. Sb.55 (1961), 125–174 (in Russian); Amer. Math. Soc. Transl.53 (1961), 23–80.

    MathSciNet  Google Scholar 

  5. F. H. Brownell and C. Clark,Asymptotic distribution of the eigenvalues of the lower part of the Schrödinger operator spectrum, J. Math. Mech.10 (1961), 31–70.

    MATH  MathSciNet  Google Scholar 

  6. T. Kato,Perturbation Theory for Linear Operators, 2nd edition, Springer, 1976.

  7. J. B. McLeod,The distribution of the eigenvalues for the hydrogen atom and the similar cases, Proc. London Math. Soc.11 (1961), 139–158.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Nagase,On the asymptotic behavior of resolvent kernels for elliptic operators, J. Math. Soc. Japan25 (1973), 464–474.

    MATH  MathSciNet  Google Scholar 

  9. A. Pleijel,On a theorem of P. Malliavin, Israel J. Math.1 (1963), 166–168.

    Article  MATH  MathSciNet  Google Scholar 

  10. F. Riesz and B. Sz-Nagy,Functional Analysis (English translation), New York, Frederick Unger, 1955.

    Google Scholar 

  11. D. Robert,Propriétés spectrales d’opérateurs pseudo-différentiels, Comm. Partial Differ. Equ.3 (1978), 755–826.

    Article  MATH  Google Scholar 

  12. G. V. Rozenbljum,The distribution of the discrete spectrum for singular differential operators, Dokl. Akad. Nauk SSSR202 (1972), 1012–1015 (in Russian); Soviet Math. Dokl.13 (1972), 245–249.

    MathSciNet  Google Scholar 

  13. G. V. Rozenbljum,An asymptotic of the negative discrete spectrum of the Schrödinger operator, Mat. Zametki21 (1977), 399–407 (in Russian); Math. Notes Acad. Sci. USSR21 (1977), 222–227.

    MATH  MathSciNet  Google Scholar 

  14. H. Tamura,The asymptotic distribution of discrete eigenvalues for Schrödinger operators, J. Math. Soc. Japan29 (1977), 189–218.

    Article  MathSciNet  Google Scholar 

  15. H. Tamura,Asymptotic formulas with sharp remainder estimates for bound states of Schrödinger operators, II, J. Analyse Math., to appear.

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Tamura, H. Asymptotic formulas with sharp remainder estimates for bound states of Schrödinger operators, I. J. Anal. Math. 40, 166–182 (1981). https://doi.org/10.1007/BF02790161

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